Early delay with hopf bifurcation

Abstract

The collection of case studies [5], which owes a lot to Bulirsch's inspiration, was based on rather elementary mathematics. The prerequisite to work on the exercises was the kind of calculus that prevailed mathematical education until 20 years ago. That is, no computer support was needed. Today relevant software packages are in general use, which has opened access to a much broader range of possible cases to study. The immense pedagogical value of the classic analytical approach remains untouched, but computational tools with additional applications must be added. In some way, modern simulation tools make it much easier to bridge the gap between elementary mathematics and current research. This holds in particular for nonlinear dynamics, where computational methods enable rapid experimental approaches into exciting phenomena. This is the broader context of the present paper. © 2008 Springer-Verlag Berlin Heidelberg.